If $A(G)$ is the adjacency matrix of a graph $G$ with $n$ vertices and $D^{-1/2}(G)$ is the diagonal matrix of reciprocals of square roots of vertex degrees, then the Kemeny's constant of $G$ is $K(G)=\sum_{i=2}^{n}\frac{1}{1-\lambda_i}$, where $\lambda_2,\lambda_3, \ldots, \lambda_n$ are all but the largest eigenvalue of $D^{-1/2}(G)A(G)D^{-1/2}(G)$. We use an approach based on determinants of particular tridiagonal matrices admitting certain periodicity to provide a closed formula for the Kemeny's constant of a cylinder octagonal chain graph, where a graph in question is obtained from a linear octagonal chain graph by identifying the lateral edges. In this way we present the correct result of [S. Zaman, A. Ullah, Kemeny's constant and global mean first passage time of random walks on octagonal cell network, Math. Meth. Appl. Sci., 46 (2023), 9177--9186] that for the graphs in question calculated the multiple of Kirchhoff index instead.